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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 757 · 40 questions
TalentJR

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

NameDateTime takenScore ___ / 40
  1. 1.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 10 (d) 1
  2. 2.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  3. 3.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 66 (c) 22 (d) 198
  4. 4.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 14 (c) 126 (d) 45
  5. 5.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 7 (d) 12
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 92? (a) 9 (b) 20 (c) 19 (d) 18
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 13 (b) 14 (c) 3 (d) 15
  8. 8.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 46 (c) 36 (d) 45
  9. 9.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 52 (c) 43 (d) 34
  10. 10.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  11. 11.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 10 (d) 11
  12. 12.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 448 (b) 565 (c) 564 (d) 555
  13. 13.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 189 (c) 63 (d) 21
  14. 14.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 39 (c) 13 (d) 42
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 4 (b) 6 (c) 3 (d) 5
  16. 16.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 348 (c) 349 (d) 304
  17. 17.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 10 (c) 33 (d) 30
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 88? (a) 19 (b) 20 (c) 8 (d) 18
  19. 19.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 630 (c) 639 (d) 640
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 18 (b) 9 (c) 19 (d) 20
  21. 21.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 57 (c) 18 (d) 162
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 14 (b) 9 (c) 11 (d) 13
  23. 23.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 193 (b) 192 (c) 200 (d) 183
  24. 24.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 261 (c) 252 (d) 262
  25. 25.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 346 (b) 411 (c) 402 (d) 412
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 18 (d) 19
  27. 27.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 21 (c) 63 (d) 7
  28. 28.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  29. 29.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
  30. 30.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 100 (c) 90 (d) 99
  31. 31.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 20 (c) 63 (d) 60
  32. 32.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 5 (b) 2 (c) 4 (d) 3
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 69? (a) 6 (b) 17 (c) 16 (d) 18
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 9 (b) 8 (c) 11 (d) 10
  36. 36.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 5 (d) 4
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 87? (a) 8 (b) 16 (c) 14 (d) 17
  38. 38.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 440 (b) 543 (c) 552 (d) 553
  39. 39.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 27 (c) 24 (d) 8
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 15 (b) 13 (c) 3 (d) 14

Answer key

  1. 2
  2. 9
  3. 66
  4. 42
  5. 8
  6. 19
  7. 14
  8. 45
  9. 43
  10. 4
  11. 9
  12. 564
  13. 63
  14. 39
  15. 5
  16. 348
  17. 30
  18. 19
  19. 639
  20. 19
  21. 54
  22. 13
  23. 192
  24. 261
  25. 411
  26. 19
  27. 21
  28. 6
  29. 7
  30. 99
  31. 60
  32. 8
  33. 4
  34. 17
  35. 10
  36. 4
  37. 16
  38. 552
  39. 24
  40. 14

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